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What you will learn from this videoWhat you will learn
- We'll learn how to express numbers in scientific notation.
- We'll also learn how to carry out operations with numbers expressed in scientific notation.
- And we'll discover that this knowledge can help us measure planets, climb mountains, and even go on a cruise! Let's explore!
- Discussion Questions
Before Video
How do you write the numbers 1 million, 1 billion, and 1 trillion?ANSWER1,000,000; 1,000,000,000; 1,000,000,000,000
7, 10, and 13, respectively; the number of place values is one more than the number of zeros.
10^{7}, 10^{10}, and 10^{13}
Use negative exponents (10^{-1}, 10^{-2}, and 10^{-3})
Long distances such as those between planets are measured in many kilometers, or distances between galaxies are measured in light-years; lengths that are very small fractions of a meter, such as amoebae or atoms.
After Video
Which expression shows an example of scientific notation: 40x10^{2} or 4.0x10^{3}?ANSWERBoth expressions represent 4,000, but only the second number is in scientific notation.
5.0x10^{4}; there are 4 place values from after the 5 to the right of the ones place.
3.6x10^{4}; there are 4 place values from after the 3 to the right of the ones place.
First, make sure that the exponents of the two numbers are the same. Then, I can add and subtract the values before the powers of ten, and keep the same power of 10 in the final sum or difference. Then I may have to put the sum or difference back in scientific notation.
I can multiply or divide the numbers before the powers of ten, and separately multiply or divide the powers of 10. I may have to write the product or quotient in scientific notation at the end.
- Vocabulary
- Scientific notation DEFINE
A number written as two parts: the digits, with the decimal point placed after the first digit, multiplied by a power of ten.
- One trillion DEFINE
A whole number with the digit 1 followed by 12 zeros (1,000,000,000,000); one thousand billions.
- Power DEFINE
A base with an exponent, representing repeated multiplication. For example, the power 10^{4} has base 10 and exponent 4, and is equivalent to 10 × 10 × 10 × 10, or 10,000.
- Decimal place DEFINE
The position of a digit to the right of a decimal point.
- One billion DEFINE
A whole number with the digit 1 followed by 9 zeros (1,000,000,000); one thousand millions.
- Negative exponent DEFINE
An exponent that is less than zero. For example, 10^{-3} has exponent –3 and is equivalent to 0.001, which has three decimal places.
- Scientific notation DEFINE
- Reading Material
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- Practice Number Problems
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